Aspheric surfaces, which can be defined generally as surfaces that depart from planes, cylinders, and spheres, present a number of challenges to their measurement beyond those of surfaces having simpler forms. Despite the increased difficulty of their measurement, aspheric surfaces must often be measured to accuracies similar to the accuracies at which surfaces of simpler forms are measured. Particularly problematic for the measurement of aspheric surfaces are large variations in local curvatures and slopes of the aspheric surfaces, which can be difficult to both capture and compare to a datum.
Among conventional surface measurement techniques, optical wavefront sensing generally provides for measuring limited size areas (i.e., subapertures) of test surfaces to high accuracy. A plurality of such subaperture measurements is often required to measure the entirety of the test surfaces. Redundant data within regions of overlap between adjoining subaperture measurements can be used to compensate for positioning uncertainty and other differences between the measurements by “stitching” the subaperture measurements together to form composite measurements of the test surfaces.
However, the range of surface variations that can be accommodated by conventional wavefront sensing techniques is limited. Generally, a measurement wavefront is generated in a reference shape, such as a spherical shape, that approximates the expected shape of the test surface to which it is directed. Upon encountering the test surface (e.g., reflecting from the test surface), the shape of the measurement wavefront is aberrated in accordance with any differences between the actual shape of the test surface and the original shape of the measurement wavefront. Wavefront sensors record the aberrations in the returning measurement wavefront. The curvature and slope variations of many aspheric surfaces can produce aberrations in such measurement wavefronts that are beyond the range of many wavefront sensors or beyond the apertures of the optics that convey the measurement wavefronts to the sensors.
Approaches for extending the range of surface variations that can be accommodated by conventional wavefront sensing techniques include reducing the size of the subapertures and adjusting the reference shape of the measurement wavefront to better match the intended shape of the individual subaperture surface areas under test. Reducing the size of the subaperture measurements increases the number of subaperture measurements, which typically increases the attendant amount of processing for stitching the subapertures together as well as the uncertainty of the stitched measurement. Adjusting the reference shape of the measurement wavefront increases sources of error and measurement ambiguity because the shape adjustments themselves must be measured or otherwise determined so that the reference shape can be used as a datum against which the aberrations in measurement wavefront can be compared.
Another conventional surface measurement technique, single-point profilometry, uses a probe (e.g., mechanical or optical probe) for measuring one point on the test surface at a time. While the probe itself generally takes measurements along a single dimension, the relative motions between the probe and the test surface must also be measured in other relative dimensions to relate the different measurements of the probe to each other and to the intended shape of the test surface. For measuring aspheric surfaces, particularly with optical probes, motions along/about both rotational and translational axes are generally required to position the probe substantially normal to the different measured points on the aspheric surface. The measurements of the multiple axes are difficult to achieve to required accuracy, and the measurement of a large number of individual points to cover the test surface with sufficient resolution is time consuming.